I bought an older house and there are 1 inch pipes running from my hot water heater, across the basement then up to the bathroom on the second floor. The pipe also goes a round-about way and there is a lot of excess pipe that can be removed. Needless to say, it takes a LONG time to get hot water in the bathroom and obviously wastes a lot of water. I want to reduce the 1 inch pipe to half inch, take out all the excess, and reconnect to the 1 inch pipe going up the wall to the bathroom. My concern is that I will lose pressure particularly in the shower. Thoughts?
Reducing pipe size will certainly reduce the amount of cold water sitting in the pipe, but it will also reduce the pressure at any given flow .vs. an equivalent larger pipe. However, you are proposing to shorten (and likely remove some elbows) from the pipe as well as change the size, and then it's very much "it depends" - there are online calculators for pressure drop you can use to compare options, for instance, but they would need type of pipe, length or equivalent length (where each elbow counts for extra equivalent length) pressure and flow to calculate a result.
How much that's an issue will depend on the type of pipe (smooth plastic flows much better than lumpy corroded galvanized iron) the supply pressure, and the demand at the end of the pipe.
It sounds like replacing all the pipe is not convenient. If it was, then 1/2" PEX "home runs" have a considerable benefit since they flow pretty well but have low volume. If this is galvanized iron or the like, and feeding only the one bathroom group, I would suggest 3/4" PEX for the easily replaceable (and shortened) part unless you live in one of the places with absurd plumbing restrictions against modern plastic pipe.
If the pipe is 1" to supply many other groups (other bathroom(s), kitchen, laundry), then think carefully about where it makes sense to have 1" pipe (due to large flow demand) and where it does not.